equivalence relation on a set breaks it into disjoint sets. does 'disjointness' make sense in classes. specifically, given a category, isomorphism classes of objects makes sense or not. can it be so that initially we start with a class of objects,but equivalence classes form a set.
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As I see, Scott's trick is helpful your attempt. – Hanul Jeon Jul 09 '14 at 13:45
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If the answers (and the links there) in the duplicate do not answer your question, consider editing your question to clarify what's missing and ping me. There are probably other threads on the site as well dealing with the topic, though. – Asaf Karagila Jul 09 '14 at 18:27